In the past few years the cooperative sensing in cognitive radio networks (CRNs) has attracted considerable attention because of its high reliability. But a large number of cooperative users produce a huge overhead in the reporting process. In this paper, we propose a new scheme to reduce the sensing overhead in CRNs, called low-overhead cooperative sensing scheme (LCS). In this scheme, we only allow those users, which detect the presence of the PU report the sensing results. Then we use a pre-sensing sequential detection technology to decrease the whole sensing time T. Considering the preload sensing slots, we derive a formula to express the overall miss detection probability. In order to minimize the average time of spectrum sensing (AT), we design a rule to protect primary transmissions over the Rayleigh fading channel. Simulation results show that the proposed algorithm can achieve superiority and efficiency of the LCS scheme. It is also seen from the results that our algorithm can reach the given sensing accuracy for CRNs.